Nanoshell-mediated laser surgery simulation for prostate cancer treatment
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- Feng, Y., Fuentes, D., Hawkins, A. et al. Engineering with Computers (2009) 25: 3. doi:10.1007/s00366-008-0109-y
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Laser surgery, or laser-induced thermal therapy, is a minimally invasive alternative or adjuvant to surgical resection in treating tumors embedded in vital organs with poorly defined boundaries. Its use, however, is limited due to the lack of precise control of heating and slow rate of thermal diffusion in the tissue. Nanoparticles, such as nanoshells, can act as intense heat absorbers when they are injected into tumors. These nanoshells can enhance thermal energy deposition into target regions to improve the ability for destroying larger cancerous tissue volumes with lower thermal doses. The goal of this paper is to present an integrated computer model using a so-called nested-block optimization algorithm to simulate laser surgery and provide transient temperature field predictions. In particular, this algorithm aims to capture changes in optical and thermal properties due to nanoshell inclusion and tissue property variation during laser surgery. Numerical results show that this model is able to characterize variation of tissue properties for laser surgical procedures and predict transient temperature fields comparable to those measured by in vivo magnetic resonance temperature imaging techniques. Note that the computational approach presented in the study is quite general and can be applied to other types of nanoparticle inclusions.
KeywordsLaser-induced thermal therapyNanoparticlesProstate cancerLaser-tissue interactionBioheat transferFinite element method
The latest statistics shows that cancer remains one of the leading causes of death in the United States . However, advances in nanotechnology and its applications in biomedical science and engineering over the past two decades have enabled numerous innovative and more effective cancer diagnosis and treatment modalities [3, 7, 10]. Treatment by traditional surgical resection procedures are a surgeon’s standard approach for removal of well-defined primary tumors in non-vital regions. This technique is extremely invasive and usually associated with high morbidity. In contrast, thermal therapies employing a variety of heat sources including laser, focused ultrasound, and microwaves have benefits over conventional cancer treatment alternatives [12, 13, 19, 25, 26]. These treatment therapies are minimally invasive and can provide an alternative option to treat solid tumors embedded in vital regions. Technological advancements, such as actively cooled applicators and high power diode lasers, have made laser-induced thermal therapy more efficient, economical, and safer than other thermal therapeutic modalities. Some advantages include that laser-induced thermal therapy can be used to treat tumors more rapidly than other modalities and have more control over perfusion effects. Additionally, lasers do not require a complicated setup that involves grounding pads and can be incorporated safely into any imaging environment, including MRI, with minimal induced image artifacts. The interaction between multiple probes for treating larger tumors can be synergistic and fully compatible with MRI for online monitoring.
On the other hand, nanoshell-mediated laser surgery is able to direct thermal energy into target regions delivered by optical fibers to provide a lethal dose of heat while minimizing damage to surrounding tissue . In particular, laser surgery promises effective treatment of small, poorly-defined metastases or other tumors embedded within vital regions. In this study, we consider a special class of nanoparticles known as nanoshells, which can act as intense infrared absorbers which increase the thermal deposition of laser energy into tumors. In particular, nanoshells provide a potential means to (a) enhance the delivery of laser-induced thermal energy via distributing the heat source from the fiber to the surrounding vasculature and/or, (b) provide a highly conformal and targeted approach to laser-induced thermal therapy in which normal tissue is spared and tumor tissue is ablated with a high level of specificity. Typically nanoshells consist of a concentric spherical dielectric (silica) core and a thin metal coating (Au) shell. The diameters of nanoshells are usually in the 110 to 120 nm range and have been shown to be effective mediated agents to control the temperature field. Nanoshells possess a highly tunable plasmon resonance which determines the particle’s scattering and absorbing properties. The plasmon resonance, one of the nanoshell’s optical properties, can be tuned across a broad range of the light spectra from the ultra-violet to the infrared by controlling the ratio between the radius of the core and the thickness of the shell layer [1, 11]. When nanoshells are injected to the target region, laser-induced thermal energy can be delivered to specified locations and greatly enhance heat absorption in tumor regions due to the change of optical properties in the tissue .
To design optimal nanoshell-mediated laser surgical protocols, it is crucial to accurately characterize the optical, thermal, and biological response of tissues to therapies [20, 21]. The major challenge is that these properties can be difficult to measure and vary over time during the treatment due to biological alteration in tissues. The goal of this paper is to present a novel nested-block optimization algorithm for nonlinear transient bioheat transfer model to simulate laser surgery in the presence of nanoshells and with consideration of dynamic changes in optical and thermal properties of the tissue due to biological alteration. In this study, a three-dimensional finite element nonlinear transient bioheat transfer model with input of laser-tissue interaction calculation from Monte Carlo fluence model is constructed. Numerical results show that this model can reliably characterize changes in tissue properties and accurately predict temperature fields comparable to those measured by in vivo magnetic resonance temperature imaging (MRTI) technique. Although the validation experiments are conducted for treating prostate tumors inoculated on SCID (severely compromised immuno-deficient) mice, the computational approach presented in the study is quite general and can be applied to other types of cancer treatment. Similar optimization strategies are also used in a dynamic data-driven framework for real-time surgical control .
2 Nanoshell-mediated laser surgery
2.1 Tumor preparation and inoculation
2.2 External heating and nanoshell inclusion
Similar to previous work , nanoshells were employed in conjunction with extracorporeal laser irradiation to enhance thermal deposition. Nanoshells were injected into the mouse tail vein 24 h prior to laser irradiation to enable adequate accumulation in the tumor volume. Nanoshells (furnished by Nanospectra Biosciences Inc. Houston, TX) are composed of a silica core (with a diameter of 110 nm) and an outer gold shell (thickness of 15 nm). The shell geometry was optimized to enable maximum absorption at wavelength 808 nm to enhance thermal deposition. Figure 1b illustrates the distribution and geometry of the nanoshells employed in laser therapy experiments.
By tuning the ratio of the core diameter and shell thickness, nanoshells can be made to absorb or scatter light at a desired wavelength across visible and near-infrared (NIR) wavelengths. This optical tunability permits optimal design of laser surgical protocols with a peak optical absorption in the NIR region. For instance, laser surgery for deeper tissue requires light in the NIR region where tissue has the highest transmissivity. The ability of gold-nanoshells to convert strongly absorbed light into localized heat can be exploited for the targeted laser therapy of cancer. Thus, effective targeting of nanoshell bioconjugates specifically to cancer cells combined with the high absorption cross-section of the nanoshells in the laser excitation region, generates increased temperatures sufficient to produce irreversible cell and tissue damage to subcutaneous tumors while keeping laser energy at a lower level so that cells outside of the target region are minimally damaged.
2.3 Temperature measurement
3 Mathematical and computational models
Simulating laser surgery and making reliable predictions of the temperature field requires two major modeling components: a bioheat transfer model for the tissue and a laser source term that characterizes thermal energy deposited into the tissue. Since the optical properties of nanoshells can be designed by adjusting the ratio between the diameter of the silica core and the thickness of the gold shell, tissue properties such as the absorption and scattering coefficients can be controlled then with inclusion of nanoshells. In this section, we discuss the mathematical and computational models for bioheat transfer and laser-tissue interaction.
3.1 Bioheat transfer model
The mathematical representation of the temperature distribution in the tissue incorporates both the Pennes bioheat equation for the thermal effects of local blood perfusion and an expression for laser energy as a thermal source. We consider the case of external heating provided by a laser source on the surface of the tumor.
3.2 Laser-heating model
Derived from the light diffusion approximation for monoenergetic neutral particles by solving the transport equation , (2) is valid when the scattering coefficient is much larger than the absorption coefficient (μs ≫ μa), which is the case in most of the soft tissues. The basic assumption in our case is that the light is emitted from a single point in a diffuse and isotropic manner. In addition, this model only accounts for scattered light, i.e., the primary light is ignored. This assumption is reasonable if the region of interest is far from the source. For external heating, these assumptions may be violated. In our case, the light from the laser beam was collimated as it enters the tissue and is incident against the skin with a flat beam spot between 0.5 mm and 1.0 cm in diameter.
the absorption coefficient, μa, the average number of photons absorbed per unit length,
the scattering coefficient, μs, the average number of photons scattered per unit length, and
the anisotropic factor, g, the expected value of the cosine of the deflection angle.
All three quantities depend on light wavelength, temperature, and space, due to heterogeneity of the tissue. However, the space dependency is usually ignored. Thus, μa, μs, and g are typically given as functions of light wavelength and temperature only. It has been found that values of these three quantities remain fairly constant for temperatures below 70°C .
The Monte Carlo simulation for laser irradiation starts with following the random paths of many individual photons by sampling probability distributions. The main idea is described as follows. The algorithm starts by initiating a photon with a weight of W = 1 and a position and direction in space. A random number between 0 and 1 is then generated and used as a value of a mean free path length by correlating it to the associated probability distribution. The photon is then moved with this length in its current direction. Then, the algorithm checks if the photon is still in the tissue. If it is not, the internal reflection for this particular photon is done. Otherwise, a portion of the photon, W · μa/μt, is assumed to be absorbed at that location, the weight is updated and then two more random numbers are generated to obtain the new azimuthal angle and the deflection angle by again correlating the random numbers to the respective probability distribution. This process is repeated until the photon’s weight has reached some cutoff weight. To conserve energy, a roulette scheme is employed here to decide if the photon should be discarded or left in with an update of its weight.
3.3 Nested-block optimization algorithm
In this section, we present a nested-optimization algorithm that applies to the Pennes bioheat transfer model . The goal is to capture dynamic changes in tissue properties due to biological alteration as well as nanoshell inclusion. In order to achieve this goal, the objective function, (5), for the calibration problem is defined as the difference in space-time norm between the computed temperature field, T(x, t), and the temperature field obtained from the MRTI experiments, Texp(x, t), integrated over the entire biological domain Ω and time duration of interest [0, τ]. The computed temperature field T(x, t) is an implicit function of the bioheat transfer model parameters β, a vector that consists of the location of the laser probe, absorption and scattering coefficients, and parameters in conductivity and perfusion functions.
The main question to be addressed in this section is how to approximate the full optimization problem efficiently so that the prediction can be made prior to the next data arrival. In other words, the speed of computation needs to be faster than the rate of data acquisition, at least faster than the time duration of the operation. The optimization problem can be formally stated as:
In order to speed up solution time for the approximation, (3) is replaced by a sequence of smaller problems with less historical data in the time dimension.
3.4 Computational implementation
The nonlinear transient bioheat transfer model is implemented using a finite element discretization in space and finite difference in time using the Crank-Nicolson scheme.
Both bioheat transfer and optimization modules are implemented in parallel using an h−p finite element method built upon an in-house code and can be executed efficiently on a multi-processor machine. The framework of this adaptive finite element code has been developed and thoroughly tested over last two decades . Computations were carried out using Linux clusters hosted at the Texas Advanced Computing Center at Austin. Each computing node has two Xeon Intel Duo-core 64-bit/2.66GHz processors. Using up to 50 processors, we are able to make real-time predictions two minutes ahead, which only takes 10 s computing time.
Data acquired for calibration are shown in Fig. 2. Figure 2a is a 49 × 56 pixel MRI image of a mouse tumor. The field of view is 4 × 6 cm2 and the thickness associated with the image is 3 mm. An external heat source was applied to a mouse tumor. Sixty thermal images were acquired at every 5 s. A single time instance of the thermal images is shown in Fig. 2c. An overlay of the thermal image onto the geometry is shown in Fig. 2b.
Model parameters used in Pennes bioheat transfer model
1,045 [kg m−3]
3,840 [ J kg−1K−1]
3,600 [J kg−1K−1]
Numerical values of thermal conductivity and blood perfusivity used in Pennes bioheat transfer model at the beginning of calibration 
k(u) = k0 + k1 atan(k2(u−k3))
ω(u) = ω0 + ω1 atan(ω2(u−ω3))
0.561 [J s−1m−1K−1]
0.255 [k g−1s−1m−1]
0.0427 [J s−1m−1K−1]
−0.137 [k g−1s−1m−1]
Figure 5d and f illustrate a cut-line comparison of the MRTI data to the FEM prediction using the isotropic laser source term and the Monte Carlo source term. The FEM model with uncalibrated parameters seems to produce inaccurate results compared with MRTI data, which strongly indicates that the tissue properties are changed due to the introduction of nanoshells.
An early study  shows that the model of bioheat transfer with a laser heating source term is anticipated to be relatively less sensitive to the attenuation coefficients of the laser source term as compared to the thermal conductivity and blood perfusivity coefficients. Thus, more changes in the blood perfusivity and tissue conductivity are expected than in absorption and scattering coefficients in the calibration process.
5 Discussion and conclusions
The extent of thermal damage associated with traditional laser therapies is limited by thermal diffusion in the tissue. Most conventional laser therapies, other than photodynamic therapy, do not permit selective destruction of tumor tissue while preserving the surrounding healthy tissue. In order to circumvent the limitations of traditional laser therapies employed in prostate cancer treatment, nanoshells were employed to enhance the thermal deposition and selectivity of thermal damage.
In this study, a new computational methodology for solving the Pennes bioheat transfer equation which incorporates a nested-block optimization algorithm is proposed. This methodology is used to simulate the transient temperature field during laser surgery on a prostate tumor inoculated on the back of SCID mice. The numerical simulations for this test case are in good agreement with the MRTI data from the surgical procedure but required several iterations through the calibration process. For the single test case presented herein the calibration process stabilized after 30 time steps (150 seconds into the surgery).
A flexible Monte Carlo based formulation for the fluence in the laser source term is incorporated in the Pennes bioheat equation, which is solved by a finite element method. This formulation is considerably more general than the classical approach allowing for non-homogeneous and anisotropic tissues, and extends the range of validity to include more complex tumor geometry. Preliminary results using this more general laser model show only modest variation (lest than 5%) in the temperature field when compared to results produced using a classical formulation for the fluence. We anticipate the new formulation will be a more significant factor in the analysis as we investigate more complex tumor geometry from the perspective of laser source modeling. Additional validation tests involving more specimens with different laser treatments protocols are underway to further refine this methodology.
The computer model developed in this study for laser-induced thermal therapy is capable of predicting the temperature due to laser heating in a prostate tumor with nanoshell inclusion by incorporating changes in the absorption and scattering effects. Using this model, optimal hyperthermia protocols can be developed. With maturity of nano-technology such as nanoshell injection and a reliable computational model, the outcome of laser surgery for cancer treatment will become more controllable and predictable. MRTI provides an in vivo measurement tool for mapping the spatiotemporal temperature elevation in the tumor during and following laser therapy. This technique for temperature measurement has resolution of less than 1°C. With the nested-block optimization algorithm presented in this study, tissue properties can be accurately characterized during the course of a surgical operation and resulting in more reliable prediction of temperature field and treatment outcomes.
The support of this work by the National Science Foundation under grant CNS-0540033 and by National Institutes of Health under Small Animal Imaging Facility core grant CA 16672 are gratefully acknowledged.